Abstract

The problem of stability of mixed convection flow in an air-filled tallvertical differentially heated channel is considered when the cross-channeltemperature difference is of the order of a hundred degrees Kelvin. It isshown that the realistic nonlinear fluid properties variation associated withlarge temperature gradient leads to significant deviations from the flowscenarios predicted using conventional constant-property Boussinesqapproximation. In the Boussinesq limit of small temperature gradients theconduction state becomes unstable with respect to shear-driven disturbances ofa primary flow. In contrast, when the fluid properties are allowed to vary, anew buoyancy-driven instability may arise. These two physically distinctinstabilities can co-exist and compete over a wide range of parameters (suchas the Grashof and Reynolds numbers and non-dimensional temperature differencebetween the channel walls) governing the problem. This enables a richdiversity of resulting flow patterns that evolve both in space and time. Innearly natural convection regimes (with a cubic primary velocity profile) theshear-driven instability is found to be absolute (convection cells occupy thefull channel volume), while in predominantly forced convection regimes withrelatively large pressure gradient along the channel (Poiseuille-type flows)the shear-driven instability is known to be convective with convection cellscarried away by the primary flow. In contrast, for small to moderate values ofthe Reynolds number, the buoyancy instability reveals its convective naturewith disturbances propagating downwards regardless of the direction of theapplied external pressure gradient. The goal of this study is twofold: first,to provide an insight into the physics of various instabilities arising inmixed convection channel flows and, second, to determine the accurate boundaryseparating regions of absolute and convective instabilities in themulti-parameter space of the mixed convection problem. Analytical results areconfirmed by direct numerical integration of the disturbance equations andresulting flow fields are presented for both shear- and buoyancy-driveninstabilities.